The S-kernel: A measure of symmetry of objects |
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Authors: | Bertrand Zavidovique [Author Vitae],Vito Di Gesù [Author Vitae] |
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Affiliation: | a IEF, Université Paris XI, ORSAY, France b DMA, Università di Palermo, Italy |
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Abstract: | In this paper we introduce a new symmetry feature named “symmetry kernel” (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorithm validation. |
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Keywords: | Symmetry transforms Symmetry measure Erosion Correlation Feature extraction |
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